She can't win. Kathelia's a know it all. She doesn't have Hornet's inventions (and even with Hornet using them, she can see that this is a mess). She doesn't have Alina's grace. She doesn't have Helya's competition genius (and the new princesses don't even look like they're cursed yet, Eupheria must not have been accounting for their arrival). 

Kathelia's got a keen mind though. Even if she can't win herself, she can be a queen-maker. She can give Adila a chance. The moment is there. She knows Adila can't hold onto the Caduceus, maybe nobody here can, save perhaps Mother, and on the order of [i]extremely bad[/i] plans, handing the staff of pure creativity to the void of pure destruction was a real list topper. But chaos was a good state of things, and better by far than Eupheria's controlled chaos. They needed to shake her. 

So, she did the only thing she could and sent Euphie a direct magical broadcast from across the room. "Eupheria, I got Alina back from your doorth" she brags, her voice broadcast by magic right to Eupheria's ears (there's no way she could shout above this normally). "I sthtopped my thithter from falling into your trap. I hope you liked the drama, I did it for you. And now I'm gonna find a way to cheat your game too. All your magic'th no match for a smart princeth." She gives Eupheria a little cheshire grin, showing off her shiny braces in a way that screams come get me even though there's nothing that's putting her ahead of the princess pack. It's not about that, it's about having Eupheria look Kathelia's way for less than half a second and thinking about her and not anything else. That's all she needed to do.
[Keep busy: 4+1+2=7. It works, but there will be reprisal at the end.]

Go get her Adila.